1. Introduction

The "Rotate Array" problem is a common task in array manipulation, which tests the ability to rotate elements in an array efficiently. The challenge involves shifting the elements to the right by a specified number of steps, adjusting the array's order accordingly. This problem is a great example of applying simple algorithms to achieve efficient data reorganization.

Problem

Given an integer array nums, the task is to rotate the array to the right by k steps, where k is a non-negative integer. This means that each element in the array should be moved k positions to the right, with the elements at the end of the array wrapping around to the front.

2. Solution Steps

1. Normalize k to prevent unnecessary rotations if k is larger than the array's length.

2. Reverse the entire array.

3. Reverse the first k elements.

4. Reverse the remaining n-k elements, where n is the length of the array.

5. The array will be rotated k steps to the right as required.

3. Code Program

def rotate(nums, k):
    n = len(nums)
    k %= n

    def reverse(i, j):
        while i < j:
            nums[i], nums[j] = nums[j], nums[i]
            i += 1
            j -= 1

    reverse(0, n - 1)
    reverse(0, k - 1)
    reverse(k, n - 1)

# Example Usage
nums = [1,2,3,4,5,6,7]
rotate(nums, 3)
print(nums)  # Output: [5,6,7,1,2,3,4]

nums = [-1,-100,3,99]
rotate(nums, 2)
print(nums)  # Output: [3,99,-1,-100]